I’m a little confused here - as this new device uses details that are already working on a different device. I also use DAVdroid on my Nexus 5 without issue. Same server, and on another device with the same configuration details…

Sorry to also bother you with this topic… But I have the same issue. And it doesn’t matter if I write the well-known redirection to /remote.php/carddav/ with trailing slash at the end or without.
This worked all very well until the last update of DavDroid.Today I wanted to add my account again but run into this issue.
I’m on Cyanogenmod 11-20141125-NIGHTLY-hammerhead

I was bumping my head with debugging logs and trying to find out the reason for ‘Method not allowed’ and issue #12 helped me to understand I need two account and then discovered about ‘well-known’ mechanim, so I suggest to put this info as FAQ entry considering that Davdroid and ownCloud must be quite popular combo.